Wikipedia:Reference desk/Archives/Science/2024 December 6
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December 6
[edit]Geodesics for Massive and Massless Particles
[edit]In general relativity, do massive and massless particles follow the same geodesic? Why or why not? Malypaet (talk) 23:19, 6 December 2024 (UTC)
- According to the Einstein field equations, the worldline traced by a particle not subject to external, non-gravitational forces is a geodesic. Each particle follows its own worldline. Two particles that share their worldline are at all times at the same location and so have identical velocities. --Lambiam 08:46, 7 December 2024 (UTC)
- A massless particle must follow a null geodesic and massive particle must follow a time-like geodesic (in my limited understanding). catslash (talk) 22:20, 7 December 2024 (UTC)
- So a massive particle with a velocity infinitely close to that of a photon (under the influence of a massive object) will have a geodesic infinitely close to that of the photon, right? Or is there another explanation and which one? Malypaet (talk) 22:11, 9 December 2024 (UTC)
- I believe that is correct (perhaps there is an expert to hand who could confirm this?). catslash (talk) 23:42, 9 December 2024 (UTC)
- In some frame of reference, the massive particle is at rest and so its spacetime interval along its geodesic is as
spaceliketime-like as can be (and thereby as non-null-like as can be for a non-tachyonic particle). So it depends on the point of view of the observer. Simplifying the case to special relativity and considering a particle traveling with speed in the x-direction, the spacetime interval between two events separated by a time is given by: - In frames of reference in which approaches the interval can become arbitrarily small, making it experimentally indistinguishable from that of a massless particle. --Lambiam 07:40, 12 December 2024 (UTC)
- @User:Lambian, could you re-read the spacetime interval section? I reckon that if there exists a frame of reference in which an interval is purely a time difference, then it is time-like, and if there exists a frame of reference in which the interval is purely a difference in location, then it is space-like. catslash (talk) 10:14, 12 December 2024 (UTC)
- Yes, I used the wrong term, now corrected. --Lambiam 07:30, 13 December 2024 (UTC)
- @User:Lambian, could you re-read the spacetime interval section? I reckon that if there exists a frame of reference in which an interval is purely a time difference, then it is time-like, and if there exists a frame of reference in which the interval is purely a difference in location, then it is space-like. catslash (talk) 10:14, 12 December 2024 (UTC)
- In some frame of reference, the massive particle is at rest and so its spacetime interval along its geodesic is as
- I believe that is correct (perhaps there is an expert to hand who could confirm this?). catslash (talk) 23:42, 9 December 2024 (UTC)